Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, ACB = 90° and AC = 15 cm.

Question

Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, ACB = 90&#xB0; and AC = 15 cm.

Philoid · Accepted Answer

In right ∆ACB using pythagorous theorem:

(AB)² = (AC)² + (BC)²

(17)² = (15)² + (BC)²

BC = 8 cm

Perimeter of quad ABCD = AB+BC+CD+DA = 17+8+12+9 = 46 cm

Area of right angled ∆ACB =

⇒ = 60 cm²

Now in equilateral ∆ACD

Let a, b and c are the sides of triangle and s is

the semi-perimeter, then its area is given by:

A = where [Heron’s Formula]

= = 18

A=

A = = cm²

Hence, area of quad ABCD =60+54 =114 cm²